Two $2$ cm thick steel plates $($of thermal conductivity, k $=43$ W$/$mK and thermal diffusivity $1\mathrm{.}17$x$10^-5$ m$^2/$s$,)$ are placed one on top of the other whilst wet. They are laid flat on the ground, and left outside over night, when the temperature falls to $.$ The following morning, a worker needs one of the plates but they are stuck together by the frozen water between them. In an effort to melt the ice, the worker brings a large hairdryer and blows hot air, at $50\backslash$deg C$,$ onto the exposed surface of the upper plate. The surface heat transfer coefficient at the top surface is estimated to be $40$ W$/$m$^2$K$.$ Determine the length of time the hot air must be blown onto the surface before the two plates separate.